The following are true of invariance:

• It is involved in proportional reasoning.


• It is the multiplicative relationship between the numerator and denominator of a fraction.


• It is the multiplicative relationship between the two quantities being compared within a ratio or rate.


• Equivalent fractions and ratios share the same "within" multiplicative relationship. The "within" relationship remains invariant.


• A factor of change can be used to determine the within multiplicative relationship in equivalent ratios and rates.


• In a rate, the invariant relationship compares quantities of different units.

Use the link below to further study invariance with an interactive example of equivalent fractions.

Invariance Activity

Both of the ratios below simplify to one to three. One to three is the invariant relationship for these two ratios.

For the relationship described below, the cups of applesauce is always two and one-half times the pounds of apples.

The two fractions below are not equivalent since the relationship between their numerators and denominators varies.